DR. S. CHAPMAN ON THE SOLAR AND LUNAR 
68 
The correction to the calculated magnetic variations produced by a given atmo¬ 
spheric motion, due to self-induction, may be considered at this stage. In place of a 
rime factor cos (n£ + e 0 ), as given by the method of § 22, the factor cos (nt + e 0 — e m n ) 
must be used, where* 
(105) 
tan e m 
n _ 
27T 
86,400 
4 t rfblpe 
2m +1 
m being the degree of the harmonic with which the time factor is associated. If we 
take 5 . 10“ 6 as a mean value of pe throughout the day and night, the following 
values of e m " are yielded by the formula (105). 
e : , 2 = 40°, e 4 3 = 44°, e 5 4 = 47°, 
e, 2 = 49°, e 3 3 = 51°, e 4 4 = 52°. 
These figures are only rough, since the non-uniform conductivity may considerably 
affect the theoretical formula (105). It may be noticed that the lag of phase, owing 
to self-induction, increases with the frequency of the harmonic, so that self-induction 
cannot explain the apparent increase of phase with frequency which is observed in 
the solar diurnal magnetic variation (Table F). 
Self-induction will also diminish the amplitudes of the magnetic variations by a 
factor cos e m n . This will not greatly affect the relative magnitudes of the various 
magnetic harmonics, but it will affect our estimate of the magnitude of pe in § 24, 
and of the heating effects in § 25. The calculated value of pe would appear to be 
increased on this account by 30 or 40 per cent., and this, again, would slightly 
increase the above values of e. 
Taking into account the above phase changes due to self-induction, the calculated 
time factors in the pressure variations are modified as follows :— 
(106) 
ed = 30°, 
®T = 44°, 
(107) (Solar) sin (2t — 115°), 
(108) (Lunar) sin(2£— 62°). 
When these are compared with (104) and (103), the “ calculated — observed ” phase 
differences are found to be 
(109) (Solar) +181°, (Lunar) +233°. 
These values almost suggest that a mistake in sign has crept into the calculation 
of the magnetic from the pressure variations, but the signs have been carefully 
* Cf. Maxwell’s ‘ Electricity and Magnetism, 1 II., § 672, or Schuster, ‘Phil. Trans.,’ A, vol. 208, 
p. 172. 
